Most Home Improvement Project requires us to calculate areas so we know how much material (e.g. carpet, tiles, wallpaper, paint) to order. Materials are expensive so we wouldn't want to waste money buying more than needed. Also, it's important to buy enough materials so you don't have to waste your time going back to the store to buy more in the middle of your project, plus there might not be the same color/hue available and then your materials would be mismatched and look awful!
Solving Area of Rectangle floor:
Measure a Floor in Square Feet -- powered by eHow.com
Finding Area of trapezoid bay window:
How to Measure for Floor Tiling -- powered by eHow.com